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\(C^1\) connecting lemmas. (English) Zbl 0947.37018
Summary: Like the closing lemma, the connecting lemma is of fundamental importance in dynamical systems. Hayashi recently proved the \(C^1\) connecting lemma for stable and unstable manifolds of a hyperbolic invariant set. In this paper, we prove several very general \(C^1\) connecting lemmas. We simplify Hayashi’s proof and extend the results to more general cases.

MSC:
37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
37C75 Stability theory for smooth dynamical systems
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